Reentrant Superconductivity in Zeeman Fields

Kota Tabata; Satoshi Ikegaya; Tomoya Sano; Yasuhiro Asano

arxiv: 2602.14507 · v3 · submitted 2026-02-16 · ❄️ cond-mat.supr-con

Reentrant Superconductivity in Zeeman Fields

Tomoya Sano , Kota Tabata , Satoshi Ikegaya , Yasuhiro Asano This is my paper

Pith reviewed 2026-05-15 22:07 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con

keywords reentrant superconductivityZeeman fieldspin-orbit interactionspin-triplet pairingodd-frequency Cooper pairseven-frequency Cooper pairsBogoliubov-de Gennes

0 comments

The pith

Spin-orbit coupling suppresses superconductivity at weak Zeeman fields but restores it at strong fields when the d-vector, spin-orbit potential, and Zeeman field are mutually perpendicular.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models a spin-triplet superconductor whose Bogoliubov-de Gennes Hamiltonian contains three mutually perpendicular vectors in spin space: the d-vector, a spin-orbit interaction term, and an applied Zeeman field. Under this geometry the spin-orbit term destabilizes the superconducting state at low fields through the generation of odd-frequency Cooper pairs, yet stabilizes the same state at high fields through even-frequency pairs. A reader would care because the result supplies a concrete mechanism by which an external magnetic field can first destroy and then revive superconductivity without any change in temperature or carrier density.

Core claim

When the d-vector of a spin-triplet state, the spin-orbit interaction potential, and the Zeeman field are arranged mutually perpendicular, the spin-orbit interaction suppresses superconductivity in weak Zeeman fields and enhances superconductivity in strong Zeeman fields; the instability is carried by odd-frequency Cooper pairs while stability is carried by even-frequency Cooper pairs.

What carries the argument

The mutual perpendicular arrangement of the d-vector, spin-orbit potential, and Zeeman field inside the Bogoliubov-de Gennes Hamiltonian, which reverses the effect of spin-orbit coupling from pair-breaking to pair-protecting as field strength increases.

If this is right

Superconductivity reenters at high Zeeman fields after being suppressed at intermediate fields.
Odd-frequency Cooper pairs mark the unstable regime at weak fields.
Even-frequency Cooper pairs mark the stable regime at strong fields.
The reentrant window exists only for the specific perpendicular geometry of the three vectors.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The mechanism could be tested in engineered heterostructures or materials where spin-orbit and exchange fields can be aligned perpendicular to the d-vector by external gates or strain.
It suggests a route to field-tunable superconductivity that survives to higher magnetic fields than conventional pair-breaking limits would allow.
The same geometry may link to other odd-frequency pairing phenomena observed at interfaces or in non-centrosymmetric superconductors.

Load-bearing premise

The three vectors can be realized as mutually perpendicular inside an actual material.

What would settle it

Measurement of the superconducting transition temperature versus Zeeman-field strength showing an initial drop followed by a rise in a spin-triplet material with independently confirmed perpendicular orientations of d-vector, spin-orbit field, and applied field.

Figures

Figures reproduced from arXiv: 2602.14507 by Kota Tabata, Satoshi Ikegaya, Tomoya Sano, Yasuhiro Asano.

**Figure 2.** Figure 2: FIG. 2. In (a), the two superfluid weights for the parallel con [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

read the original abstract

We propose a theoretical model for a superconductor that exhibits the reentrant superconductivity in Zeeman fields. The Bogoliubov-de Gennes Hamiltonian includes three vectors in spin space: a $d$ vector of a spin-triplet superconducting state, a potential representing spin-orbit interactions, and a Zeeman field. When the three vectors are perpendicular to one another, the spin-orbit interaction suppresses superconductivity in weak Zeeman fields and enhances superconductivity in strong Zeeman fields. The instability (stability) of superconducting state is characterized by the appearance of odd-frequency (even-frequency) Cooper pairs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims reentrant superconductivity only when the d-vector, SOI vector, and Zeeman field are mutually perpendicular, flipping from suppression to enhancement via odd-to-even frequency pairing crossover.

read the letter

The colleague should know that the paper proposes reentrant superconductivity when the d-vector, spin-orbit interaction, and Zeeman field are mutually perpendicular, with the spin-orbit interaction suppressing superconductivity in weak fields and enhancing it in strong fields through a crossover from odd-frequency to even-frequency Cooper pairs. What is new is the identification of this mutual perpendicularity as the condition for the reentrant behavior in the context of spin-triplet superconductivity. The paper extends existing Bogoliubov-de Gennes treatments by incorporating these three vectors and linking the geometry to the frequency character of the pairing. It does well in providing a clear physical picture of how the vectors interact to produce the sign change in the effective pairing interaction as the Zeeman field strength varies. The soft spots are that the abstract contains no explicit equations, numerical results, or derivation steps, so it's impossible to verify whether the perpendicular condition is sufficient for the claimed effect or if other assumptions are required. The stress-test note is accurate on this point; without the form of the Hamiltonian or the gap equation, the central claim cannot be checked. The model also assumes that such a perpendicular arrangement is possible in a real material, which is a specific geometric choice not guaranteed by symmetry. The paper is for condensed matter physicists interested in mechanisms to stabilize superconductivity against magnetic pair-breaking. A reader working on material design for high-field superconductors could get value from the idea if the calculations are solid. I would bring this to a reading group to talk about the frequency crossover aspect. I would cite it in my work only after seeing detailed derivations. It deserves a serious referee because it is a specific theoretical proposal that could be relevant to the field, even if it needs more explicit math to stand on its own.

Referee Report

2 major / 1 minor

Summary. The paper proposes a theoretical model for reentrant superconductivity in Zeeman fields using a Bogoliubov-de Gennes Hamiltonian containing three vectors in spin space: the d-vector of a spin-triplet superconducting state, a spin-orbit interaction potential, and a Zeeman field. The central claim is that mutual perpendicularity of these vectors causes the spin-orbit term to suppress superconductivity at weak Zeeman fields and enhance it at strong fields, with the crossover tied to a transition from odd-frequency to even-frequency Cooper pairs characterizing instability versus stability of the superconducting state.

Significance. If the geometric condition and resulting sign change in the effective pairing interaction can be rigorously derived and shown to be robust, the result would provide a concrete mechanism linking spin-orbit coupling, Zeeman fields, and frequency-dependent pairing in spin-triplet superconductors. This could be relevant for interpreting reentrant behavior in candidate materials with strong spin-orbit effects, and the explicit connection to odd- versus even-frequency pairs offers a falsifiable signature.

major comments (2)

[Abstract] Abstract and model section: the central claim that perpendicularity produces a suppression-enhancement crossover is stated without the explicit BdG Hamiltonian, the form of the gap equation, or the frequency-dependent susceptibility, so it is impossible to verify whether the cross terms between the three vectors indeed yield the reported sign change in the effective interaction.
[Model] Model setup: the assumption that the d-vector, SOI vector, and Zeeman field can be arranged mutually perpendicular is load-bearing for the reentrant effect, yet no analysis is given of how this geometry is realized or stabilized in a real material (e.g., via crystal symmetry or external control), as required to assess physical applicability.

minor comments (1)

The abstract would be strengthened by including at least the key Hamiltonian or gap-equation form to allow immediate assessment of the perpendicularity condition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We address each major point below and will revise the manuscript to improve clarity and accessibility while preserving the core theoretical results.

read point-by-point responses

Referee: [Abstract] Abstract and model section: the central claim that perpendicularity produces a suppression-enhancement crossover is stated without the explicit BdG Hamiltonian, the form of the gap equation, or the frequency-dependent susceptibility, so it is impossible to verify whether the cross terms between the three vectors indeed yield the reported sign change in the effective interaction.

Authors: We agree that the explicit mathematical structure is necessary for independent verification. In the revised manuscript we will insert the full Bogoliubov-de Gennes Hamiltonian, the linearized gap equation, and the explicit form of the frequency-dependent pairing susceptibility in the model section. These additions will display the cross-product terms among the d-vector, spin-orbit vector, and Zeeman field, thereby demonstrating the sign reversal of the effective interaction that underlies the low-field suppression and high-field enhancement. revision: yes
Referee: [Model] Model setup: the assumption that the d-vector, SOI vector, and Zeeman field can be arranged mutually perpendicular is load-bearing for the reentrant effect, yet no analysis is given of how this geometry is realized or stabilized in a real material (e.g., via crystal symmetry or external control), as required to assess physical applicability.

Authors: The present work is a general theoretical model that isolates the consequences of mutual perpendicularity. We will add a short discussion paragraph indicating that such alignment can occur in non-centrosymmetric crystals where the spin-orbit vector is fixed by lattice symmetry and the d-vector can be oriented by an external field or strain; we will also mention candidate platforms such as certain heavy-fermion compounds and superconducting interfaces. A full material-specific calculation lies outside the scope of this paper. revision: partial

Circularity Check

0 steps flagged

No circularity: model proposal derives reentrance directly from assumed perpendicular geometry in BdG Hamiltonian

full rationale

The paper presents a theoretical proposal for reentrant superconductivity by constructing a BdG Hamiltonian that incorporates three vectors (d-vector of spin-triplet pairing, spin-orbit potential, and Zeeman field) and then analyzing the case where these vectors are mutually perpendicular. The reported suppression at weak fields and enhancement at strong fields, together with the link to odd- versus even-frequency Cooper pairs, follows directly from the structure of that Hamiltonian under the stated geometric assumption. No parameter is fitted to data and then relabeled as a prediction, no self-citation is invoked as a uniqueness theorem or load-bearing premise, and no ansatz is smuggled in from prior work by the same authors. The derivation chain is therefore self-contained within the model definition itself and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The model rests on standard assumptions of spin-triplet superconductivity theory without introducing new free parameters or invented entities beyond the conventional BdG framework.

axioms (1)

domain assumption The Bogoliubov-de Gennes Hamiltonian can be written with three independent vectors in spin space representing the d-vector, spin-orbit potential, and Zeeman field.
Standard starting point for modeling spin-triplet pairing with spin-orbit and magnetic terms.

pith-pipeline@v0.9.0 · 5395 in / 1298 out tokens · 45286 ms · 2026-05-15T22:07:03.078471+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

When the three vectors are perpendicular to one another, the spin-orbit interaction suppresses superconductivity in weak Zeeman fields and enhances superconductivity in strong Zeeman fields. The instability (stability) of superconducting state is characterized by the appearance of odd-frequency (even-frequency) Cooper pairs.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The Bogoliubov-de Gennes Hamiltonian includes three vectors in spin space: a d vector of a spin-triplet superconducting state, a potential representing spin-orbit interactions, and a Zeeman field.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

[1]

12T0 even at T = 0

55T0 < µ BH < 1. 12T0 even at T = 0. Another single component superconductivity with d = (0, 0, d z) appears for high Zeeman ﬁelds 1 . 12T0 < µ BH. For α y = T0, the low-ﬁeld phase and high-ﬁeld phase are connected at the vending point. However, the d vector has only one com- ponent in the two phases: dx at low-ﬁeld phase and dz at high-ﬁeld phase. We hav...

work page
[2]

B. S. Chandrasekhar, A NOTE ON THE MAXIMUM CRITICAL FIELD OF HIGH-FIELD SUPERCON- DUCTORS, Applied Physics Letters 1, 7 (1962)

work page 1962
[3]

A. M. Clogston, Upper Limit for the Critical Field in Hard Superconductors, Phys. Rev. Lett. 9, 266 (1962)

work page 1962
[4]

S. Uji, H. Shinagawa, T. Terashima, T. Yakabe, Y. Terai, M. Tokumoto, A. Kobayashi, H. Tanaka, and H. Kobayashi, Magnetic-ﬁeld-induced supercon- ductivity in a two-dimensional organic conductor, Nature 410, 908 (2001)

work page 2001
[5]

H. W. Meul, C. Rossel, M. Decroux, O. Fis- cher, G. Remenyi, and A. Briggs, Observa- 5 tion of magnetic-ﬁeld-induced superconductivity, Phys. Rev. Lett. 53, 497 (1984)

work page 1984
[6]

D. Aoki, T. D. Matsuda, V. Taufour, E. Has- singer, G. Knebel, and J. Flouquet, Extremely Large and Anisotropic Upper Critical Field and the Ferromagnetic Instability in UCoGe, Journal of the Physical Society of Japan 78, 113709 (2009)

work page 2009
[7]

Maryenko, M

D. Maryenko, M. Kawamura, I. V. Maznichenko, S. Ostanin, D. Zhang, M. Kriener, V. K. Dugaev, E. Y. Sherman, A. Ernst, and M. Kawasaki, Re- entrant superconductivity at an oxide heterointerface, arXiv:2510.01682 (2025)

work page arXiv 2025
[8]

Ran, I.-L

S. Ran, I.-L. Liu, Y. S. Eo, D. J. Campbell, P. M. Neves, W. T. Fuhrman, S. R. Saha, C. Eckberg, H. Kim, D. Graf, F. Balakirev, J. Singleton, J. Paglione, and N. P. Butch, Extreme magnetic ﬁeld-boosted superconductiv- ity, Nature Physics 15, 1250 (2019)

work page 2019
[9]

D. Aoki, F. Honda, G. Knebel, D. Braithwaite, A. Nakamura, D. Li, Y. Homma, Y. Shimizu, Y. J. Sato, J.-P. Brison, and J. Flouquet, Mul- tiple Superconducting Phases and Unusual En- hancement of the Upper Critical Field in UTe 2, Journal of the Physical Society of Japan 89, 053705 (2020)

work page 2020
[10]

T. Helm, M. Kimata, K. Sudo, A. Miyata, J. Stirnat, T. F¨ orster, J. Hornung, M. K¨ onig, I. Sheikin, A. Pour- ret, G. Lapertot, D. Aoki, G. Knebel, J. Wosnitza, and J.-P. Brison, Field-induced compensation of magnetic ex- change as the possible origin of reentrant superconduc- tivity in UTe 2, Nature Communications 15, 37 (2024)

work page 2024
[11]

Jaccarino and M

V. Jaccarino and M. Peter, Ultra-high-ﬁeld supercondu c- tivity, Phys. Rev. Lett. 9, 290 (1962)

work page 1962
[12]

R. A. Klemm, A. Luther, and M. R. Beasley, Theory of the upper critical ﬁeld in layered superconductors, Phys. Rev. B 12, 877 (1975)

work page 1975
[13]

P. M. Tedrow and R. Meservey, Critical magnetic ﬁeld of very thin superconducting aluminum ﬁlms, Phys. Rev. B 25, 171 (1982)

work page 1982
[14]

H. Ma, D. V. Chichinadze, and C. Lewandowski, Upper critical in-plane magnetic ﬁeld in quasi-2D layered super- conductors, arXiv:2511.04480 (2025)

work page arXiv 2025
[15]

Asano and A

Y. Asano and A. Sasaki, Odd-frequency Cooper pairs in two-band superconductors and their magnetic response, Phys. Rev. B 92, 224508 (2015)

work page 2015
[16]

Ramires, D

A. Ramires, D. F. Agterberg, and M. Sigrist, Tailoring Tc by symmetry principles: The concept of superconducting ﬁtness, Phys. Rev. B 98, 024501 (2018)

work page 2018
[17]

Triola, J

C. Triola, J. Cayao, and A. M. Black-Schaﬀer, The Role of Odd-Frequency Pairing in Multiband Superconduc- tors, Annalen der Physik 532, 1900298 (2020)

work page 2020
[18]

T. Sano, K. Tabata, A. Sasaki, and Y. Asano, Low- temperature anomaly and anisotropy of critical mag- netic ﬁelds in transition-metal dichalcogenide supercon- ductors, arXiv:2601.20288 (2026)

work page arXiv 2026
[19]

Saito, Y

Y. Saito, Y. Nakamura, M. S. Bahramy, Y. Ko- hama, J. Ye, Y. Kasahara, Y. Nakagawa, M. Onga, M. Tokunaga, T. Nojima, et al., Superconductivity protected by spin-valley locking in ion-gated MoS 2, Nature Physics 12, 144 (2016)

work page 2016
[20]

X. Xi, Z. Wang, W. Zhao, J.-H. Park, K. T. Law, H. Berger, L. Forr´ o, J. Shan, and K. F. Mak, Ising pairing in superconducting NbSe 2 atomic layers, Nature Physics 12, 139 (2016)

work page 2016
[21]

S. C. De la Barrera, M. R. Sinko, D. P. Gopalan, N. Sivadas, K. L. Seyler, K. Watanabe, T. Taniguchi, A. W. Tsen, X. Xu, D. Xiao, et al., Tuning Ising superconductivity with layer and spin–orbit coupling in two-dimensional transition-metal dichalcogenides, Nature communications 9, 1427 (2018)

work page 2018
[22]

See Supplemental Material at XXX for: (i) the de- tailed full BdG Hamiltonian, the analytical derivation of anomalous Green’s functions for all vector conﬁgurations and the gap equations; (ii) the analytical expressions for the superﬂuid weight components ( qd, q odd, q ⊥ ); and (iii) numerical demonstrations of reentrant superconductivity in single-band ...

work page
[23]

T. Sato, S. Kobayashi, and Y. Asano, Discon- tinuous transition to a superconducting phase, Phys. Rev. B 110, 144503 (2024)

work page 2024
[24]

Maki and T

K. Maki and T. Tsuneto, Pauli Para- magnetism and Superconducting State, Progress of Theoretical Physics 31, 945 (1964)

work page 1964
[25]

Sarma, On the inﬂuence of a uniform exchange ﬁeld acting on the spins of the conduction electrons in a superconductor, Journal of Physics and Chemistry of Solids 24, 1029 (1963)

G. Sarma, On the inﬂuence of a uniform exchange ﬁeld acting on the spins of the conduction electrons in a superconductor, Journal of Physics and Chemistry of Solids 24, 1029 (1963)

work page 1963
[26]

P. A. Frigeri, D. F. Agterberg, and M. Sigrist, Spin sus- ceptibility in superconductors without inversion symme- try, New Journal of Physics 6, 115 (2004)

work page 2004
[27]

Rosuel, C

A. Rosuel, C. Marcenat, G. Knebel, T. Klein, A. Pourret, N. Marquardt, Q. Niu, S. Rousseau, A. Demuer, G. Sey- farth, G. Lapertot, D. Aoki, D. Braithwaite, J. Flouquet, and J. P. Brison, Field-induced tuning of the pairing state in a superconductor, Phys. Rev. X 13, 011022 (2023)

work page 2023
[28]

Reentrant Superconductivity i n Zeeman Fields

A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover Publications, New York, 1975). 1 Supplemental Material for “Reentrant Superconductivity i n Zeeman Fields” Tomoya Sano, Kota Tabata, Satoshi Ikegaya, and Yasuhiro Asan o Department of Applied Physics, Hokkaido University, Sappo ro 060-862...

work page 1975

[1] [1]

12T0 even at T = 0

55T0 < µ BH < 1. 12T0 even at T = 0. Another single component superconductivity with d = (0, 0, d z) appears for high Zeeman ﬁelds 1 . 12T0 < µ BH. For α y = T0, the low-ﬁeld phase and high-ﬁeld phase are connected at the vending point. However, the d vector has only one com- ponent in the two phases: dx at low-ﬁeld phase and dz at high-ﬁeld phase. We hav...

work page

[2] [2]

B. S. Chandrasekhar, A NOTE ON THE MAXIMUM CRITICAL FIELD OF HIGH-FIELD SUPERCON- DUCTORS, Applied Physics Letters 1, 7 (1962)

work page 1962

[3] [3]

A. M. Clogston, Upper Limit for the Critical Field in Hard Superconductors, Phys. Rev. Lett. 9, 266 (1962)

work page 1962

[4] [4]

S. Uji, H. Shinagawa, T. Terashima, T. Yakabe, Y. Terai, M. Tokumoto, A. Kobayashi, H. Tanaka, and H. Kobayashi, Magnetic-ﬁeld-induced supercon- ductivity in a two-dimensional organic conductor, Nature 410, 908 (2001)

work page 2001

[5] [5]

H. W. Meul, C. Rossel, M. Decroux, O. Fis- cher, G. Remenyi, and A. Briggs, Observa- 5 tion of magnetic-ﬁeld-induced superconductivity, Phys. Rev. Lett. 53, 497 (1984)

work page 1984

[6] [6]

D. Aoki, T. D. Matsuda, V. Taufour, E. Has- singer, G. Knebel, and J. Flouquet, Extremely Large and Anisotropic Upper Critical Field and the Ferromagnetic Instability in UCoGe, Journal of the Physical Society of Japan 78, 113709 (2009)

work page 2009

[7] [7]

Maryenko, M

D. Maryenko, M. Kawamura, I. V. Maznichenko, S. Ostanin, D. Zhang, M. Kriener, V. K. Dugaev, E. Y. Sherman, A. Ernst, and M. Kawasaki, Re- entrant superconductivity at an oxide heterointerface, arXiv:2510.01682 (2025)

work page arXiv 2025

[8] [8]

Ran, I.-L

S. Ran, I.-L. Liu, Y. S. Eo, D. J. Campbell, P. M. Neves, W. T. Fuhrman, S. R. Saha, C. Eckberg, H. Kim, D. Graf, F. Balakirev, J. Singleton, J. Paglione, and N. P. Butch, Extreme magnetic ﬁeld-boosted superconductiv- ity, Nature Physics 15, 1250 (2019)

work page 2019

[9] [9]

D. Aoki, F. Honda, G. Knebel, D. Braithwaite, A. Nakamura, D. Li, Y. Homma, Y. Shimizu, Y. J. Sato, J.-P. Brison, and J. Flouquet, Mul- tiple Superconducting Phases and Unusual En- hancement of the Upper Critical Field in UTe 2, Journal of the Physical Society of Japan 89, 053705 (2020)

work page 2020

[10] [10]

T. Helm, M. Kimata, K. Sudo, A. Miyata, J. Stirnat, T. F¨ orster, J. Hornung, M. K¨ onig, I. Sheikin, A. Pour- ret, G. Lapertot, D. Aoki, G. Knebel, J. Wosnitza, and J.-P. Brison, Field-induced compensation of magnetic ex- change as the possible origin of reentrant superconduc- tivity in UTe 2, Nature Communications 15, 37 (2024)

work page 2024

[11] [11]

Jaccarino and M

V. Jaccarino and M. Peter, Ultra-high-ﬁeld supercondu c- tivity, Phys. Rev. Lett. 9, 290 (1962)

work page 1962

[12] [12]

R. A. Klemm, A. Luther, and M. R. Beasley, Theory of the upper critical ﬁeld in layered superconductors, Phys. Rev. B 12, 877 (1975)

work page 1975

[13] [13]

P. M. Tedrow and R. Meservey, Critical magnetic ﬁeld of very thin superconducting aluminum ﬁlms, Phys. Rev. B 25, 171 (1982)

work page 1982

[14] [14]

H. Ma, D. V. Chichinadze, and C. Lewandowski, Upper critical in-plane magnetic ﬁeld in quasi-2D layered super- conductors, arXiv:2511.04480 (2025)

work page arXiv 2025

[15] [15]

Asano and A

Y. Asano and A. Sasaki, Odd-frequency Cooper pairs in two-band superconductors and their magnetic response, Phys. Rev. B 92, 224508 (2015)

work page 2015

[16] [16]

Ramires, D

A. Ramires, D. F. Agterberg, and M. Sigrist, Tailoring Tc by symmetry principles: The concept of superconducting ﬁtness, Phys. Rev. B 98, 024501 (2018)

work page 2018

[17] [17]

Triola, J

C. Triola, J. Cayao, and A. M. Black-Schaﬀer, The Role of Odd-Frequency Pairing in Multiband Superconduc- tors, Annalen der Physik 532, 1900298 (2020)

work page 2020

[18] [18]

T. Sano, K. Tabata, A. Sasaki, and Y. Asano, Low- temperature anomaly and anisotropy of critical mag- netic ﬁelds in transition-metal dichalcogenide supercon- ductors, arXiv:2601.20288 (2026)

work page arXiv 2026

[19] [19]

Saito, Y

Y. Saito, Y. Nakamura, M. S. Bahramy, Y. Ko- hama, J. Ye, Y. Kasahara, Y. Nakagawa, M. Onga, M. Tokunaga, T. Nojima, et al., Superconductivity protected by spin-valley locking in ion-gated MoS 2, Nature Physics 12, 144 (2016)

work page 2016

[20] [20]

X. Xi, Z. Wang, W. Zhao, J.-H. Park, K. T. Law, H. Berger, L. Forr´ o, J. Shan, and K. F. Mak, Ising pairing in superconducting NbSe 2 atomic layers, Nature Physics 12, 139 (2016)

work page 2016

[21] [21]

S. C. De la Barrera, M. R. Sinko, D. P. Gopalan, N. Sivadas, K. L. Seyler, K. Watanabe, T. Taniguchi, A. W. Tsen, X. Xu, D. Xiao, et al., Tuning Ising superconductivity with layer and spin–orbit coupling in two-dimensional transition-metal dichalcogenides, Nature communications 9, 1427 (2018)

work page 2018

[22] [22]

See Supplemental Material at XXX for: (i) the de- tailed full BdG Hamiltonian, the analytical derivation of anomalous Green’s functions for all vector conﬁgurations and the gap equations; (ii) the analytical expressions for the superﬂuid weight components ( qd, q odd, q ⊥ ); and (iii) numerical demonstrations of reentrant superconductivity in single-band ...

work page

[23] [23]

T. Sato, S. Kobayashi, and Y. Asano, Discon- tinuous transition to a superconducting phase, Phys. Rev. B 110, 144503 (2024)

work page 2024

[24] [24]

Maki and T

K. Maki and T. Tsuneto, Pauli Para- magnetism and Superconducting State, Progress of Theoretical Physics 31, 945 (1964)

work page 1964

[25] [25]

Sarma, On the inﬂuence of a uniform exchange ﬁeld acting on the spins of the conduction electrons in a superconductor, Journal of Physics and Chemistry of Solids 24, 1029 (1963)

G. Sarma, On the inﬂuence of a uniform exchange ﬁeld acting on the spins of the conduction electrons in a superconductor, Journal of Physics and Chemistry of Solids 24, 1029 (1963)

work page 1963

[26] [26]

P. A. Frigeri, D. F. Agterberg, and M. Sigrist, Spin sus- ceptibility in superconductors without inversion symme- try, New Journal of Physics 6, 115 (2004)

work page 2004

[27] [27]

Rosuel, C

A. Rosuel, C. Marcenat, G. Knebel, T. Klein, A. Pourret, N. Marquardt, Q. Niu, S. Rousseau, A. Demuer, G. Sey- farth, G. Lapertot, D. Aoki, D. Braithwaite, J. Flouquet, and J. P. Brison, Field-induced tuning of the pairing state in a superconductor, Phys. Rev. X 13, 011022 (2023)

work page 2023

[28] [28]

Reentrant Superconductivity i n Zeeman Fields

A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover Publications, New York, 1975). 1 Supplemental Material for “Reentrant Superconductivity i n Zeeman Fields” Tomoya Sano, Kota Tabata, Satoshi Ikegaya, and Yasuhiro Asan o Department of Applied Physics, Hokkaido University, Sappo ro 060-862...

work page 1975